a=2, b=1 A bullet is to be tested in the laboratory to determine the drag force on it. Dependent parameter the drag force D (Newton) depends on the velocity of the bullet V(m/s), the length of the bullet L(m), sound velocity c(m/s), density of fluid ρ (kg/m3) and dynamic viscosity µ(kg/ms). Solve the problem by making the necessary assumptions and drawing the schematic figure I-Determine the nondimensional p parameters using repeating variables ii-a bullet with a speed of 9a,b m/s in air may be modelled in a water tunnel with a test section velocity of 2ab cm/s. Determine the length of the model, if the length of the bullet is 5a,b mm. The air and water temperature is 20 oC degree at 1 atm. iii- if the drag force on the model is measured to be 2,ab N, then determine the expected drag force on the bullet. Comment on dynamic similarity equivalence?
a=2, b=1
A bullet is to be tested in the laboratory to determine the drag force on it. Dependent parameter the drag force D (Newton) depends on the velocity of the bullet V(m/s), the length of the bullet L(m), sound velocity c(m/s), density of fluid ρ (kg/m3) and dynamic viscosity µ(kg/ms). Solve the problem by making the necessary assumptions and drawing the schematic figure
I-Determine the nondimensional p parameters using repeating variables
ii-a bullet with a speed of 9a,b m/s in air may be modelled in a water tunnel with a test section velocity of 2ab cm/s. Determine the length of the model, if the length of the bullet is 5a,b mm. The air and water temperature is 20 oC degree at 1 atm.
iii- if the drag force on the model is measured to be 2,ab N, then determine the expected drag force on the bullet. Comment on dynamic similarity equivalence?
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In this problem, we have the following six variables n=6. Now, the dimension of different parameters are giving below –
Assumptions: -
- Other variables are not affected by this phenomenon.
- Modal and prototype is considered to be similar,.
- Eddies' effects can be neglected.
We have three fundamentals quantity, m= 3
Hence the number of non-dimensional pie terms are = n – m = 6 – 3 = 3
Comparing M L and T terms from both side which gives,
Comparing M L and T terms from both side which gives,
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